CAKE: Preheat oven to 350℉. Grease a 9 inch cake pan or 9 x 9 square baking pan with cooking spray or butter and set aside.
STREUSEL: Combine the butter cubes, flour, brown sugar, cinnamon, and salt in a bowl. Use your hands or a fork to work the ingredients together until the mixture is easy to press together and break into large chunks, similar to play-dough (see photo above). Place in the refrigerator until ready to use.
Grate the zucchini on the small holes of a box grater and set aside. You should have about 2 cups. Place the zucchini in a fine mesh sieve and use a rubber spatula to gently press any excess water out.
Whisk together the browned butter, sugars, oil, eggs, and vanilla. Stir in the zucchini. Add the flour, baking soda, baking powder, cinnamon, and nutmeg, mixing until just combined. Spread batter evenly into prepared cake pan and set aside.
Sprinkle the streusel into chunks on top of the cake batter. Bake for 30-40 minutes until just set and a toothpick inserted into the center comes out clean. Remove from oven and place on a wire rack to cool.
GLAZE: whisk together the powdered sugar, half and half, and vanilla extract. Add more powdered sugar or half and half if needed until the glaze is a thick, pourable consistency.
Drizzle the glaze evenly over the coffee cake and serve slightly warm or at room temperature. Store leftovers in an airtight container in the refrigerator for up to 5 days.